6 ideas
Human approaches to uncertainty evolved through distinct stages: attributing chance to gods and fate, then to luck and divination, then to mathematical probability of games, then to statistical regularities in populations, then to quantum indeterminacy, and finally to chaos in deterministic systems. Each age did not replace the prior one but added a new layer of tools for handling what we cannot predict.
A system can follow exact deterministic rules with no randomness whatsoever and still be impossible to predict over time, because tiny differences in starting conditions amplify exponentially. Chaos shows that 'random-looking' behavior often hides perfectly lawful mechanics that we simply cannot measure precisely enough.
Probability has two rival interpretations: the frequentist view treats it as the long-run proportion of outcomes in repeated trials, while the Bayesian view treats it as a quantified degree of belief that updates with new evidence. Which interpretation you adopt changes what a probability statement actually means and how you reason from data.
Events that feel uncannily improbable are usually inevitable once you account for the vast number of opportunities for some coincidence to occur. The mind notices the one striking match and ignores the millions of non-matches, so 'miraculous' coincidences are predicted by the law of large numbers rather than evidence of fate.
Quantum randomness cannot be explained by hidden local variables we simply haven't discovered yet; experiments testing Bell's inequalities show correlations stronger than any local-realist theory permits. This means the uncertainty in quantum mechanics appears to be fundamental to nature rather than a gap in our knowledge.
The convention of treating a p-value below 0.05 as proof of an effect confuses 'unlikely under chance' with 'true and important,' and encourages researchers to mine data until something crosses the threshold. Real understanding requires effect sizes, replication, and judgment about prior plausibility, not a mechanical significance test.